Actually I am working on some algorithm . Taking a seed point on the surface of a polygon. And propagate it considering the linked vertives. Suppose, v1 is my seed point. It has edge with v2, v3, v4 and so on. Next I am considering the link vertices of v2, v3, v4. Next iteration considering their links and so on. Now when viewed the behaviour of propagation of a seed point, it seems at some stage of iteration, some outermost layer points meet and forms a closed edge. Definitely one or a few of the outermost layer form a closed edge. I need to know at what stage the closed edgeis formed to avoid further iteration.
Thanks for any further suggestion. Pls ask me if needs further clarification.

Actually I am working on some algorithm . Taking a seed point on the surface of a polygon. And propagate it considering the linked vertives. Suppose, v1 is my seed point. It has edge with v2, v3, v4 and so on. Next I am considering the link vertices of v2, v3, v4. Next iteration considering their links and so on. Now when viewed the behaviour of propagation of a seed point, it seems at some stage of iteration, some outermost layer points meet and forms a closed edge. Definitely one or a few of the outermost layer form a closed edge. I need to know at what stage the closed edgeis formed to avoid further iteration.
Thanks for any further suggestion. Pls ask me if needs further clarification.

Once again, using that approach, every polygon will be a 'ring'.
I don't think that's what you want.
Also, you could easily wind up with an infinite number of rings.